Management of investment portfolios has been the subject of substantial theory and research. Portfolio theory considers how wealth should be invested and how to maximize a portfolio's expected return for a given amount of portfolio risk, or equivalently minimize risk for a given level of expected return, by carefully choosing the proportions of various assets. While a certain rate of return may be expected, the valuation of individual holdings in the portfolio can depart upward or downward from that expected rate of return. This upward and downward variation from the expected value is known as variance, or volatility. Over time, securities, in theory, should have an efficient frontier for expected volatility and return. According to theory, securities with a higher expected risk will have a higher expected return.
The S&P 500 is the largest equity benchmark in the world. Trillions of dollars are either invested in this benchmark or in funds benchmarked to it. Since the yearend 1999, the broad market indices such as the S&P 500 have experienced a long period where the returns on the broad-based equity indices have underperformed. For example, an investor in the S&P 500 at yearend 1999 was down approximately 20% 10 years later at yearend 2010. It was not until late 2012 that the S&P 500 had a positive return for these yearend 1999 investors, including many large pension funds and endowments. During this same period, broad-based funds holding government or corporate debt have had positive returns with corporate debt earning more than government debt during this period. This premium was due to the extra risk of a corporate bond versus a government bond. These markets had their annual ups and downs, but over a reasonable period of time, these securities had both positive returns and differences that would be expected based on risk. Neither of these statements can be made for the equity indices such as the S&P 500 which lost value on an absolute basis and underperformed materially over a long period of time with respect to the less risky indices holding corporate or government debt.
The S&P 500, like most broad market indices, is capitalization-weighted. This means that the weight of an individual company in the index is proportional to its market capitalization relative to the other companies in the index. There are no controls in the S&P 500 to ensure that a single security or groups of securities with a common risk do not become too large a proportion of the portfolio. That is, the type of controls used in scientific fields and engineered processes where population controls are used to limit the influence that one part of a population can have on a total population being measured are not used in the broad market indices. These controls limit both positive and negative influences. In population studies, controls are used to produce a normative model of an underlying population. Because there are no controls in the benchmarks currently used to invest in equity securities, there is no assurance that these historical returns from yearend 1999 to the present are representative of equity securities in general. All that is known is that the weighting strategy (capitalization-weighting without controls) has produced below average returns for long periods of time.
The result of the major indexes since 1999 appears to be inconsistent with the main theories of the pricing of investment securities and the theory of efficient markets. Much of the work on efficient markets followed the pioneering work of Markowitz and Sharpe with later notable additions by others such as Merton. Their theories suggest that individual securities are priced at a level that is expected to produce a risk adjusted return relative to other investment securities and that, by following certain rules, a portfolio of securities has a higher probability of achieving this risk adjusted rate of return in any given period or over several periods. The rules that Markowitz and others proposed were designed to assist investors and managers in the selection of the most efficient portfolio design by analyzing various possible portfolios of the given securities.
By choosing securities that do not ‘move’ exactly together, the models show investors how to reduce their risk. The foundational model in this area is known as the Mean-Variance Model because it is based on expected returns (mean) and the standard deviation (variance) of the various portfolios. When developing the original mean variance model, Markowitz made the assumptions that a portfolio that gives maximum return for a given risk or minimum risk for a given return is an efficient portfolio. Thus, portfolios are selected using the following rules: (a) From the portfolios that have the same return, the investor will prefer the portfolio with lower risk, and (b) From the portfolios that have the same risk level, an investor will prefer the portfolio with higher rate of return. Although an individual security may underperform for a long period of time, the rules developed for efficient portfolio construction were designed to reduce this probability of underperformance with respect to the portfolio of securities.
One explanation for the inconsistency between modern portfolios and the theoretical portfolios on which the efficient market hypothesis was developed is that modern portfolios are a much greater scale and complexity than the theoretical examples. The theoretical models tend to use individual securities and describe diversification within portfolios consisting of numbers of securities that are in the single digits and low double digits. Many of the foundational papers were written before the mutual fund boom that started in the 1980s expanded in the 1990s following the creation of individual retirement accounts (IRAs) by the Employee Retirement Income Security Act (ERISA) of 1974, as well as the introduction of the first index fund in 1976. The Markowitz paper on portfolio selection published in the Journal of Finance was written in 1952. According to the first shareowner census undertaken by the New York Stock Exchange (NYSE) in 1952, only 6.5 million Americans owned common stock (about 4.2% of the U.S. population). Sharpe's paper, “A Simplified Model for Portfolio Analysis,” was written in 1963 and his book, “Portfolio Theory and Capital Markets,” was written in 1970, long before the mutual fund boom created by ERISA, globalization and modern technology, and long before investors started to recognize the unique problems of managing such large funds.
Modern portfolios manage trillions of dollars, and, in order to reduce exposure to non-systematic risk, the portfolios require thousands of securities in diverse risk groups. At this scale, building efficient portfolios has been challenging. The absolute scale of investment today by the average institution has grown exponentially. In addition, the underlying population of securities has grown in heterogeneity and complexity. The total investment in the US mutual funds was $13 trillion dollars in 2012. The US public securities is less than 20% of the total global securities by number of companies. In addition, most of the US companies are significantly dependent on the global economy. This diversity and interconnectedness is increasing every year. The need to control for the non-systematic risks imbedded in this portfolio of companies increases every year also.
This leads to several questions: 1) is the time period under which capitalization models are tested too short and should more time be allowed; 2) is the theory wrong in that risk and return are not necessarily correlated; 3) are capitalization-weighted security portfolios an inefficient design and are other examples with controls to contrast with this model needed. Put another way, there is a need for a new normative case for constructing portfolios of investment securities, a case that addresses the complexities of today's companies and the increasing size and diversity of today's funds by applying the methodology and foundational principles of Markowitz and Sharpe to the complexities of today's large-scale funds.
Current systems of classification create difficulties in building new models of potential efficient portfolios of these large-scale modern investment vehicles. These systems, similar to the foundational papers in finance, were created before the advent of large digital databases and are modeled after the databases of the time such as the Dewey Decimal System and Standard Industry Classification System. These systems categorize the entities that classify. Each is a fixed hierarchy in which each entity has a single parent; that parent has a single parent, and so on. Each parent has descriptions, but not concepts of specific intrinsic attributes that would enable an entity under one parent to be related to an entity under another parent. Without this delineation, it is hard to understand the multivariate risks to which companies are exposed and, thus, to see how many companies in a large portfolio may share a similar or related risk. These types of difficulties in classification are becoming increasingly apparent given complexities of today's companies and the increasing size and diversity of today's funds. Despite the fact that one of the biggest risks in a capitalization-weighted strategy is the lack of controls for single risk exposures, bubbles or massive non-systematic price corrections, there are currently limited tools to systematically address these problems. Thus, there is a need for a multivariate classification system enabled by current data processing capable of providing these tools and the ability to build multiple different portfolios to test the efficiency of each and test for a normative case.
Volatility
Volatility in pricing occurs continually with each fluctuation in price. Volatility is a significant factor in portfolio performance and these price fluctuations create a drag on portfolio growth. For example, daily volatility has been shown to hurt the return of leveraged exchange traded funds (ETFs). (See Tony Cooper, Alpha Generation and Risk Smoothing Using Managed Volatility (2010)).
In an effort to reduce the effects of volatility on a portfolio, various weighting schemes have been suggested. For example, one method described in U.S. Pat. No. 8,306,892 operates by calculating weights based on market capitalization, gross-domestic product, and geographic region. In another example, described in U.S. Pat. No. 8,131,620, weights a portfolio of securities are based on market capitalization and positive dividend yield. Numerous other portfolio weighting schemes exist. None of these weighting schemes fully realize the Markowitz model, specifically, that normalizing risk/return is statistical process that requires matching the number of securities and the degree of correlation between the specific securities.
Some examples, such as that described in U.S. Pat. No. 8,005,740, use North American Industry Classification System (NAICS) sectors for weighting. Weighting schemes based on NAICS or Global Industry Classification Standard (GICS) relate companies by their positions in a fixed hierarchy. There are two significant limitations of the fixed NAICS and GICS hierarchies: 1) any items without a common parent are unrelated and cannot be compared; 2) any items in the same parent can only be compared along the metrics that GICS or NAICS uses to define that group (insofar as the names of the groups indicate the metric that separates them, e.g., “consumer” vs “commercial” may relate to the customer base).
Without controls, random groups of securities can have periods of significant valuation swings, both up and down, from one time period to another. These massive swings in value may not be caused by variables such as accounting attributes or their designation of as “growth” or “value” stock. Rather, they can be caused by specific intrinsic attributes of the individual companies comprising the groups. The valuation swings could be caused by, for example, companies being long a specific commodity when the commodity suddenly loses its value; there is over-exuberance in the demand prospects for a company's or industry's product and it does not meet demand; they have long fixed-cost contracts and the actual costs available to their competitors changes; or they have over-weighted a certain asset in the product mix and that class loses its value; or other reasons.
There are many reasons for random bubbles. In some cases, they are broad market (also referred to as systematic) bubbles; in others, they are limited to a constituent group (such as an asset class or industry). There are certain events that appeared to be systematic because they created so much bias, e.g., the Internet bubble, but are non-systematic. In either case, the impact to an investor's returns can be extremely negative.
The random walk theory represents the inability to address the apparent randomness of volatility and returns in equity-based investment securities. The random walk theory states that a large random selection of equity-based investment securities will do as well as an actively-managed selection of equity-based securities. The random walk theory is the underlying reason for index funds and the broad support for passive index funds by the academic community. The random walk theory, “[t]aken to its logical extreme . . . means that a blindfolded monkey throwing darts at the stock listings could select a portfolio that would do just as well as one selected by the experts.” (B. Malkiel, A Random Walk Down Wall Street, 10th ed., 2012)
Many different weighting strategies have been proposed to deal with this problem of random volatility in equity-based investment securities. The recent underperformance of these indices to comparable debt indices has highlighted that these passive indexes are continually plagued by the same randomness hypothesis.
Historically, healthcare was also plagued by a similar randomness problem. In healthcare, this hypothesis was framed as a random patient going to a random doctor having some probability of receiving a random answer. Before modern medicine and modern statistical control groups, many believe that the probability of a random answer was very high. The healthcare industry slowly solved this problem by creating detailed patient profiles and developing statistical methodologies using information from these profiles to control for underlying characteristics of a given population. This work occurred incrementally as each disease area and governmental agencies researched and understood a series of natural biases until a well-developed field specific framework evolved.
The systems and methods described herein can be used in investment management by controlling for specific types of random events that impact the overall randomness of risk and return in investment securities. Random movements in investment securities create a drag on returns, especially large downward movements caused by events such as bankruptcy or the popping of non-systematic bubbles. In both of these cases, there is no expectation that investment securities will rebound to pre-existing levels. In both of these cases, the securities being impacted are being re-priced because of a sudden market recognition that they were overpriced.
Non-systematic bubbles and bankruptcies are associated with non-systematic factors such as the underlying intrinsic attributes of the industries, companies, or assets associated with specific investment securities. A major problem in the risk management of large portfolios of securities is the inability to control for the occurrence of these types of events. If a portfolio inadvertently over-weights in a security or groups of securities that have a common bubble or bankruptcy risk, the returns can be materially impacted by a relatively small number of securities in the portfolio. In several cases, over-weighting in specific non-systematic variables has caused systematic-like impacts on a portfolio. This was clearly the case of the Internet bubble. In calendar year 2000, the capitalization-weighted S&P 500 was down 9.09%. It was one of the worst years in S&P 500 history. In that year, there were 16 stocks that were down 49.8%, while the rest of the market was up 4.28%. Unfortunately for investors, these 16 companies, which were all in the business of moving, storing, or processing information, were 24.8% of the total portfolio.
The prior efforts to improve portfolio returns appear to have at least two problems: 1) a sub-optimal number of groups, and 2) no ability to control for variance or correlation between groups or within each group to ensure that each group operates in a predictable group-specific way. Existing large-scale heterogeneous portfolios of securities have insufficient controls on their constituent groups and neither capitalization-weighting nor even weighting solves the problem of population control.
Problems of Scale
For multiple reasons, the problems described above are particularly acute in large-scale portfolios of securities. Without both a reliable and validated system of attributes as well as a stratification system that uses a stratified composite hierarchy, it is exceptionally difficult to control for the different attributes associated with the securities. Various example reasons why management at scale is difficult are provided below.
(a) Charter limits on ownership: For many funds and fund managers, there are limits on the percentage of a company they can own. For example at 5% holdings, there are 13-D filings and oversight. Many funds will not or cannot cross that threshold.
(b) Liquidity limits on ownership: The more a fund owns of an individual security, the harder it is to sell depending on the liquidity of the shares. In addition, because of size, many funds have absolute dollar or dollar-equivalent limits on ownership. If a fund has $50 billion to invest, a $1 million investment might be considered too small.
(c) Large funds need a large number of securities to fill out a portfolio: Due to the factors identified above as well as other practical issues, a large fund needs a large number of companies to invest in due to liquidity and ownership issues. Across an economic system, there are many linkages and the larger the number of companies, the harder it is to track and oversee the potential linkages and risks that come from these linkages. A major part of these linkages are due to non-systematic attributes associated with, among other things, a company's suppliers, products, industry, operations, geographic location, etc. It is very easy for portfolios with a large number of securities to become over concentrated in non-systematic risk categories. Understanding the different potential risk groups and controlling for them is difficult without both a reliable and validated system of attributes as well as a stratified composite hierarchy to control for the different attributes.
(d) The fact that investors do not pick the universe of qualified companies to invest in: Due to the factors identified above as well as many more practical issues, large funds need to invest in large companies. The available companies in this group vary from time to time. In addition, from time to time, these securities have variable weights and aggregate differently depending on what companies exist in which category at any given point in time. In addition to changes over time, this industry, sector, or company selection varies by geography. In fact, sector differentiation may be a greater cause of price movements between geographies than the underlying currency that drives the products. For example, a US portfolio is much heavier in technology stocks than Europe of Latin America. Europe and Latin America are relatively heavy in commodities and raw materials. If a fund manager's goal is currency differentiation, it is important to control for these sector variations. First understanding the different potential risk groups that exist at any given point in time and in any specific geography or category, and then being able to control for them is difficult using currently known techniques.
(e) Attribute risk is multi-dimensional, as is the risk of concentration: Single and multiple attributes are helpful in distinguishing risks in individual companies. For example, identifying that a company is in the semi-conductor business is a differentiable risk. Furthermore, the type of semi-conductor (e.g., storage, processing, linking) is important, as are the raw materials required and the identities of the customers. These varied yet critical factors are often aggregated into one category in large-scale funds. The existing categories in current systems tend to be standardized on a global basis and are unable to differentiate between these factors. The inability to represent linked multi-attribute risks is a significant limitation for existing large-scale investment portfolios.
If portfolios, and large-scale portfolios in particular, are not better controlled, non-systematic events can appear to have systematic impact. Examples of non-systematic events are provided below. Known and existing systems do not address the underlying statistical causes for the systematic impact of the random volatility of the constituents of large-scale portfolios of securities. With improved controls, however, the impact of non-systematic events could be limited.